A334263 E.g.f. A(x) satisfies: A(x) = x - Sum_{k>=2} prime(k-1) * A(x)^k / k!.

1, -2, 9, -65, 653, -8432, 133190, -2488589, 53690330, -1313508417, 35929413073, -1086587503799, 35998774583176, -1296581783771904, 50442455219483951, -2108020240791081088, 94179374365406507609, -4479409651990684350045, 225977974437623955594777

Offset

1,2

Comments

Exponential reversion of A008578 (1 together with primes).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..200

Index entries for reversions of series

Formula

a(n) ~ -(-1)^n * n^(n-1) / (sqrt(t) * r^(n - 1/2) * exp(n)), where t = Sum_{k>=0} prime(k+1) * s^k / k! = 0.7444466039931411886049681349033665583265654464..., s = -0.835708320094278846648094879804371313211261254223... is the root of the equation Sum_{k>=1} prime(k) * s^k / k! = -1 and r = -s - Sum_{k>=2} prime(k-1) * s^k / k! = 0.34673082109620141270389189466020238662524394743... - Vaclav Kotesovec, Apr 21 2020

Mathematica

nmax = 19; CoefficientList[InverseSeries[Series[x + Sum[Prime[k - 1] x^k/k!, {k, 2, nmax}], {x, 0, nmax}], x], x] Range[0, nmax]! // Rest

Crossrefs

Cf. A007296, A008578.

Sequence in context: A099975 A292976 A334315 * A127056 A228696 A042255

Adjacent sequences: A334260 A334261 A334262 * A334264 A334265 A334266

Keyword

sign

Author

Ilya Gutkovskiy, Apr 20 2020

Status

approved